# Sig Fig: How Many Magnesium Ions in 200 kg MgO?

• STEMucator
In summary, the conversation discusses the calculation of magnesium ions in a sample of MgO with 3 significant figures. The resulting answer of 120kg for magnesium and 76kg for oxygen may seem strange due to rounding and the use of significant figures. However, it is a result of the limitations of significant figures and not a fault of the calculations.
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## Homework Statement

A 200. kg sample of MgO is given (Notice 3 sig figs). How many kg of magnesium ions would there be?

%Mg = 62%
%O = 38%

## The Attempt at a Solution

The sample of MgO given is 200.kg (3 sig figs). The percent composition of magnesium is 62% (2 sig figs). Therefore 62% of the 200.kg will be magnesium.

(62%/100%)(200.kg) = (0.62)(200.kg) = 124kg, but because the answer must have 2 sig figs, the final answer would be 120kg ( This is my suspicion ).

Notice if the kg of oxygen is calculated :

(38%/100%)(200.kg) = (0.38)(200.kg) = 76kg. This answer already has 2 sig figs, so nothing needs to be changed.

Now when added together : 120kg + 76kg = 196kg < 200.kg.

Is this result a fault of the rules or a fault of my own?

Zondrina said:
Is this result a fault of the rules or a fault of my own?

Rounding often messes the result in some way. And as significant digits are far from being perfect (generally speaking they are a poor man's way of dealing with uncertainties) there is nothing strange in the fact calculations done using them yield strange results.

1 person
Borek said:
Rounding often messes the result in some way. And as significant digits are far from being perfect (generally speaking they are a poor man's way of dealing with uncertainties) there is nothing strange in the fact calculations done using them yield strange results.

Yes, rounding leaves a sour taste every time. Thank you for the confirmation though, I just wanted to make sure.

## 1. How many significant figures should be used when calculating the number of magnesium ions in 200 kg MgO?

The number of significant figures in a measurement is determined by the precision of the measurement. Since 200 kg is a rounded value, we should use 1 significant figure in the final answer.

## 2. What is the molar mass of MgO and why is it important in calculating the number of magnesium ions?

The molar mass of MgO is 40.3 g/mol. It is important in calculating the number of magnesium ions because it is used to convert the given mass of MgO (200 kg) to moles. This allows us to use the mole ratio between MgO and Mg ions to determine the number of magnesium ions.

## 3. How many moles of MgO are in 200 kg?

To convert from mass (kg) to moles, we need to use the molar mass of MgO. 200 kg of MgO is equivalent to 4,950 moles.

## 4. What is the mole ratio between MgO and Mg ions?

The mole ratio between MgO and Mg ions is 1:1. This means that for every 1 mole of MgO, there is 1 mole of Mg ions.

## 5. What is the final answer for the number of magnesium ions in 200 kg MgO?

Using the mole ratio and the number of moles of MgO (4,950 moles), we can determine that there are 4,950 magnesium ions in 200 kg of MgO.

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